GCD-Free Algorithms for Computing Modular Inverses

Abstract

This paper describes new algorithms for computing a modular inverse e− 1 given coprime integers e and f. Contrary to previously reported methods, we neither rely on the extended Euclidean algorithm, nor impose conditions on e or f. The main application of our gcd-free technique is the computation of an RSA private key in both standard and CRT modes based on simple modular arithmetic operations, thus boosting real-life implementations on crypto-accelerated devices.